You plan to retire in $45$ years and would like to be able to spend $$4,000$ a month $($at the end of every month$)$ in retirement, and you estimate that you will live for $25$ years in retirement. How much do you need to save per month $($end of every month$)$ between now and retirement to meet your goal?

a$.$ Assume interest rate $=5\%$

i$.$ $$175\mathrm{.}52$

ii$.$ $$353\mathrm{.}01$

iii. $$337\mathrm{.}66$

iv$.$ $$2,222\mathrm{.}22$

b$.$ Assume interest rate $=10\%$

i$.$ $$41\mathrm{.}99$

ii$.$ $$606\mathrm{.}06$

iii. $$9,828\mathrm{.}96$

iv$.$ $$506\mathrm{.}30$